The latter paper of Yu makes use of a quantitative or persistent version of K-theory for algebras that have some kind of scale or length. This quantitative theory gives more refined information that is very possible to transfer using localised lifting maps like those that appear in the Higson trace. This quantitative theory has been conveniently and systematically studied by Oyono-Oyono–Yu [1]} and this gives us a framework and some general results to begin taking advantage of.
